After working on the franchise for six years, Jacobson tells PEOPLE in the new Hunger Games special issue one of her favorite parts of the job is passing on stories about the unabashed Oscar winner to her 15-year-old.

“I would say the anecdotes most often have to do with just being silly and a goofball and not letting success make you self-important,” she says, adding that it’s important “not to take yourself seriously, no matter how seriously everybody else takes you.”

Lawrence, 25, earned Jacobson’s admiration right off the bat for her stance on body image in Hollywood.

“Jen was very vocal about the tyranny of skinniness imposed on actresses, and the way in which actresses are expected to be very subhuman in their weight,” she explains.

“She really has passionate feelings about that and how destructive it is for girls,” Jacobson adds. “For her to be vocal about that when she’s a beautiful, glamorous young woman – I always really admired that.”

Jacobson specifically recalls a straightforward answer Lawrence gave to a journalist who asked about her favorite designer during press interviews for the first film in the hit franchise. The actress and Dior fashion ambassador answered simply, “I don’t know, I really just like wearing sweatpants.”

VIDEO: Jennifer Lawrence and the Cast of The Hunger Games: Mockingjay, Part 2 Say Goodbye to the Popular Franchise

Knowing Lawrence, Jacobson said she understood the comment wasn’t meant to be facetious. “It’s not that ‘I’m too good for fashion,’ it’s ‘high fashion is too good for me,’ ” the producer explains.

“I think a lot of actresses imagine themselves getting their Oscar when they’re little girls. For Jen, I think she just really loves to act,” Jacobson says, adding that for Lawrence, “fame is a byproduct, but it’s not the intention.

“If anything, it’s the downside, not the reason or reward,” she adds. “It’s almost an undesirable byproduct of doing what you love to do and being successful at it.”

The Hunger Games: Mockingjay, Part 2 hits theaters Friday.

For more on the final chapter in the franchise, check out PEOPLE’s special edition THE HUNGER GAMES: INSIDE ALL FOUR MOVIES on sale now.